Edwina Aylward

Hello! I am a second year PhD student at University College London under the supervision of Vladimir Dokchitser. I am also one of the organisers of the London junior number theory seminar.

I am interested in algebraic number theory and arithmetic geometry. More specifically, my research concerns elliptic and hyperelliptic curves, the Birch and Swinnerton-Dyer conjecture, and parity conjectures.

Previously, I did my undergraduate studies at Trinity College Dublin, and the Part III masters course at Trinity College, Cambridge. A copy of my CV is here.

Preprints

• Tamagawa numbers and positive rank of elliptic curves (April 2025).

Other writings

• Simple wild parameters and simple supercuspidal representations

  (June 2024, LSGNT mini-project 2, supervised by Beth Romano)

• Artin formalism and BSD

  (March 2024, LSGNT mini-project 1, joint with Albert Lopez-Bruch and supervised by Vladimir Dokchitser)

• The modularity theorem and the modular approach

  (May 2023, Part III essay)

• Steenrod squares and the Steenrod algebra

  (May 2022, final year undergraduate project)

Talks

• Reduction types of genus 2 curves

  (April 2025, WINGs 2025)

• Explicit regular models of hyperelliptic curves

  (March 2025, Models of Curves and Arithmetic Applications study group, UCL)

• Extended Weyl group and affine Dynkin diagrams

  (November 2024, Bruhat-Tits theory study group, KCL)

• Artin's primitive root conjecture

  (November 2024, 'Open problems in number theory' study group, UCL)

• Rank predictions: parity vs. L-value approaches

  (November 2024, Junior number theory seminar, University of Warwick)

• A survey of the Inverse Galois Problem

  (October 2024, London junior number theory seminar, KCL)

• Artin formalism and BSD

  (August 2024, YRANT VI, University of Oxford)

• Introduction to Etale cohomology

  (May 2024, Galois cohomology study group, KCL)

• Ray class fields

  (April 2024, Class field theory study group, UCL)

• Modularity theorem and Diophantine equations

  (October 2023, 10 minute presentations, UCL)

Contact

You can contact me at firstname.lastname.23@ucl.ac.uk.